A certain sum becomes 16 times in 4 years at compound interest, compounded annually. What is tue rate of interest.
No spamming and if you did spamming then I will report your every answer
Answers
Answer:
After 4 years, the amount is 16 times the principal. Here, n = 4 years. Amount = 16 P.
Step-by-step explanation:
Let the required rate of interest be R.
Consider, the principal be P for time n years.
After 4 years, the amount is 16 times the principal. Here,
n = 4 years
Amount = 16 P
We know that,
\rm Amount = P \left( 1 + \dfrac{R}{100}\right)^nAmount=P(1+
100
R
)
n
\implies \rm 16P = P \left(\dfrac{100 + R}{100}\right)^4⟹16P=P(
100
100+R
)
4
\implies \rm (2)^4 = \left(\dfrac{100 + R}{100}\right)^4⟹(2)
4
=(
100
100+R
)
4
On cancelling power 4 both sides,
\implies \rm 2 = \dfrac{100 + R}{100}⟹2=
100
100+R
On cross-multiplying both sides -
\rm \implies 100 + R = 200⟹100+R=200
\implies \rm R = 200 - 100⟹R=200−100
\boxed{\bf \therefore \: R = 100 \%}
∴R=100%